The graph of the function f(x) = (x +2)(x + 6) is shown below.

on a coordinate plane, a parabola opens up. it goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0).

what is true about the domain and range of the function?

the domain is all real numbers, and the range is all real numbers greater than or equal to –4.
the domain is all real numbers greater than or equal to
–4, and the range is all real numbers.
the domain is all real numbers such that –6 ≤ x ≤ –2, and the range is all real numbers greater than or equal to –4.
the domain is all real numbers greater than or equal to
–4, and the range is all real numbers such that –6 ≤ x ≤ –2.

  The domain is all real numbers, and the range is all real numbers greater than or equal to –4.

Step-by-step explanation:

The domain is the horizontal extent of the function. This one is defined for all real values of x.

The range is the vertical extent of the function. This one takes on any value greater than or equal to -4.

Thus, we can conclude ...

  The domain is all real numbers, and the range is all real numbers greater than or equal to –4.

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.